The Fractional SIRC Model and Influenza A

Moustafa El-Shahed,Ahmed Alsaedi

doi:10.1155/2011/480378

Abstract

This paper deals with the fractional‐order SIRC model associated with the evolution of influenza A disease in human population. Qualitative dynamics of the model is determined by the basic reproduction number, R0. We give a detailed analysis for the asymptotic stability of disease‐free and positive fixed points. Nonstandard finite difference methods have been used to solve and simulate the system of differential equations.

Highlights

Influenza is transmitted by a virus that can be of three different types, namely A, B, and C 1
The virus A is epidemiologically the most important one for human beings, because it can recombine its genes with those of strains circulating in animal populations such as birds, swine, horses, and so forth 2, 3
Over the last two decades, a number of epidemic models for predicting the spread of influenza through human population have been proposed based on either the classical susceptible-infected-removed SIR model developed by Kermack and McKendrick 4

Summary

Introduction

Influenza is transmitted by a virus that can be of three different types, namely A, B, and C 1. Over the last two decades, a number of epidemic models for predicting the spread of influenza through human population have been proposed based on either the classical susceptible-infected-removed SIR model developed by Kermack and McKendrick 4. Casagrandi et al 5 have introduced SIRC model by adding a new compartment C, which can be called cross-immune compartment, to the SIR model This cross-immune compartment C describes an intermediate state between the fully susceptible S and the fully protected R one. Jodar et al 7 developed two nonstandard finite difference schemes to obtain numerical solutions of a influenza A disease model presented by Casagrandi et al 5. We consider the fractional order SIRC model associated with the evolution of influenza A disease in human population.

Model Derivation

Equilibrium Points and Stability

Numerical Methods and Simulations